Abstract:
The National Football League (NFL) is the most popular and profitable professional sports league as it produced $12 billion turnover in 2020. The probability distributions certainly play a significant role to analyze and predict different aspect of such mega events. In this research, we aim to compare the performance of several existing distributions such as Normal, Logistic, Cauchy, Gumbel, Laplace, Johnson’s SU, Hyperbolic and Landau distribution having support from - ∞ to ∞ to model the margin of victory over point spread (M) in football games of National Football League (NFL). Besides we also intend to compare the performance of the truncated versions of some of the selected distributions having support from to to model M. We plan to present an overall comparison of the performance of non-truncated and truncated versions of the understudy distributions to model M on the basis of negative log-likelihood, Akaike's Information Criteria (AIC) and Bayesian Information Criteria (BIC). In addition, the fitting of the understudy distributions will be checked by drawing probability density functions on the histogram of the margin of victory over point spread. Finally, we will calculate the quantiles of the best fitted distribution and the probability of winning of favorite team using NFL data.
